Longitudinal vibrations of piano strings have been observed for at least seven decades, and perhaps longer. In an article about piano strings that appeared in the September 1996 issue of the JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, Harold A. Conklin, Jr. mentioned A. F. Knoblaugh's 1928 report about "wolftones" in some pianos that he (Knoblaugh) believed were caused by longitudinal vibrations. Knoblaugh never published his report, but he did present a paper about longitudinal vibrations at the 29th A.S.A. meeting (A. F. Knoblaugh, "The Clang Tone of the Pianoforte", JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, Vol. 16, P. 102 (1944).
On Aug. 11, 1970, Harold A. Conklin, Jr. was granted U.S. Pat. No. 3,523,480 for "Longitudinal Mode Tuning of Stringed Instruments". In 1983, Conklin published an article on the same subject in the JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA (Supplement 1, Vol. 73).
An article by M. Podelsak and A. R. Lee that appeared in 1987 described the percussive excitation that was expected to produce longitudinal components as well as transverse vibrations, but offered little quantitative data (M. Podelsak and A. R. Lee, "Longitudinal Vibrations in Piano Strings", JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, Supplement 1, Vol. 81, 1987).
In another article the following year, Podelsak stated that the "percussive sound-pressure components of longitudinal string vibration origin masked strongly the initial sound development, and the effect of dispersion on the attack transient of the radiated sound could not be established" (M. Podelsak and A. R. Lee, "Dispersion of Waves in Piano Strings", JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, Vol. 83, PP. 305-317, 1988). Tuning longitudinal modes, as is done in the prior art, has definite merit, however, it does not address the origins of longitudinal modes that are preferable to eliminate or reduce than to merely tune. What is missing from the prior art is a method of reducing longitudinal modes in musical instrument strings.